Nowadays every browser has an anonymous browing mode: Chrome has Incognito mode, Safari has Private Browsing, Firefox has... actually, Firefox has Private Browsing too. Whatever the name, what these browsing modes all have in common is that once the browser is closed, there is no record of which sites have been visited. That's not to say that ISPs and law enforcement agencies wouldn’t be able to determine the browsing history, but from a local point of view it is as though no browsing has taken place.
But Edge is different.
Somewhat counterintuitively, Edge actually records browsing history in InPrivate mode. More than this, by examining the WebCache file it is a relatively simple task for someone to reconstruct full browsing history, regardless of whether surfing was performed in regular or InPrivate mode.